Generally, "set plays" are almost exclusively reserved for faceoff scenarios, but once set up in the offensive zone there is a basic concept that is run and ad libbed on. And yes, getting the puck to the front of the net is the primary concern.
There are four primary offensive concepts that are run: overload, positional, behind the net, and crash/funnel.
Overload (aka triangle) - Pretty similar to the triangle offense in basketball actually; the forwards form a vaguely triangular shape with one in front of the net another in the corner and the third on the boards near the circle. The idea is to outnumber the defenders in one of the lower quadrant areas and cycle the puck around until there is an open shooting lane or passing lane to guy in front of the net. This is what the Hawks play most of the time. Once in formation you'll see the forwards start to rotate (along with the "strong side" D man [the guy on the puck side]). This favors good skating teams because if one of the players in the rotation beats his man it becomes a 2 on 1 with him and the other forward closest to the net and the "weak side" defender.
Positional - considerably less skating than an overload, they basically set up in a similar set to what they would in the defensive zone: the C in the slot, wingers in the circles/corners, and the D at the points. The idea is that you get the puck down low and find a way to pass cross ice for a one-timer. This makes the goalie and D move laterally more. The passing lanes are harder to open up than in an overload (since the passes are longer) but the passes are more effective at opening up shooting lanes.
Behind the Net - watch some old Gretzky tape, the guy lived behind the net. You get a C or winger (whomever is your best passer) in behind the net, thus splitting the responsibility of the opposing D men. Once one of the defenders attacks the puck carrier he has an outlet pass to the winger on that defender's side if the other team's C doesn't rotate quickly enough. So there will either be an open guy on the boards to that side, or that winger attacks the net uncovered and (hopefully) gets the pass on his way there. Alternatively, if neither of the D men commit to attacking the puck carrier behind the net, he can make a quick move out front for a wrap around shot or to force the C out of position in order to open a passing lane.
Crash/funnel - the idea is to get 2 or 3 forwards in front of the net and take more shots from the point looking for deflections/rebounds or get one guy on the boards trying to force a pass to the other two camping in the slot (slot = area in front of the net between the circles). This is a big bodied team scheme, you need monsters that are hard to move out from the front of the net as well as big guys who can dig the puck out from a board battle and set up the other two.
Watch some "legion of doom" (mid 90s Fliyers) clips for an idea of how to work this scheme -- easily my favorite line of all time; LeClair at LW (huge guy who could dig the puck out as well as shoot), Lindros at C (Urlacher sized mother ****** with amazingly soft hands), and the RW changed a bunch between Recchi, Brind'amour, Clarke and others. [oh, and look at the silliness of
LeClair's stick blade] I'll get around to a stick post later once we get general strategy out of the way.